You visited us 5 times! Enjoying our articles? Unlock Full Access!

Relative Velocity

Find the area...

Question

Find the area bounded by $x -$ axis and an arc of the cycloid
$x = a (2 t - sin 2 t), y = a (1 - cos 2 t)$

Open in App

Solution

for cycloid curve

Using Green's theorem

$= \int C_{1} - y d x$

$= \int_{2 π}^{0} (a (1 - c o s t) \times a (1 - c o s t)) d t$

$= a^{2} \int_{2 π}^{0} 1 - 2 c o t t - c o s^{2} t d t$

by solving
$= 3 π a^{2}$

$\Rightarrow \int C_{2} - y d x$

$\Rightarrow - \int_{2}^{0} 0 \times a (1 - c o s t) d t = 0$

$a r e a = 3 π a^{2} + 0 = 3 π a^{2}$

Suggest Corrections

Similar questions

x = a (t + sin t), y = a (1 + cos t)

x

x = \frac{π}{4}

y = sin x, y = cos x

(0 \leq x \leq \frac{π}{2})

A_{1}

A_{2}

A_{1} : A_{2}

x = a (t + sin t), y = a (1 + cos t)

f (x) = | x | - 2

g (x) = | f (x) |

A_{1}

A_{2}

A_{1}

C_{1} : y = (x - 1) e^{x}

C_{1}

(1, 0)

A_{2}

C_{1}

Join BYJU'S Learning Program